A convex lens of power 5 D and a concave lens of power 7.5 D are placed in contact with each other. What is the :(a) power of this combination of lenses?(b) focal length of this combination of lenses?

(a) Given:

Power of convex lens, $P_1$ = $+$5 D

Power of concave lens, $P_2$ = $-$7.5 D

To find: Power of this combination of lenses, $P$.

Solution:

We know that the combined power is the algebraic sum of the individual powers of the lenses.

Therefore, Power of the combination,

$P=P_1+P_2$

 $P=5+(-7.5)$

$P=5-7.5)$

$P=-2.5D$                                         

Thus, the power of the combination of the lenses is -2.5 D.

(b) The power and focal length are related as:

$P=\frac {1}{f}$

Substituting the given values, we get-

$-2.5=\frac {1}{f}$

$f=\frac {1}{-2.5}$

$f=-\frac {10}{25}$

$f=-\frac {10}{25}$

$f=-0.4m=-40cm$

Thus, the focal length of this combination of lenses is -40cm.